588 



REPORT 1893. 



(fig. 9) take Oa=l, and at any angle take Oa'=K. Join aa' . Through 

 ABCD . . . draw A A', BB', CC, . . . parallel to a a'. Then 



OA'=K.OA 

 OB'=K.OB 

 OC'=K.OC 



(3) If the two rows of points intersect in points which do not corre- 

 spond, the property of the parabola may be employed. 



Let A, B, C, . . . (fig. 10) be given segments ; take a along 

 the same line equal to nnity (or «) ; at any angle to Oa draw the line 

 O 0', where 0'a'=0'0=K (or n K). Draw a parabola having Oa and 

 O O' tangents at a and 0'. 



Fig. 10. 



(A-)0 



If A A', B B', C C, 



are tangents, 



0'A'=K.OA 

 0'B'=K.OB 

 0'C'=K.OC 



The problem of successively multiplying OA by K,, Kg, K3, ... is 

 of course practically the same as the foregoing, but may be performed in 

 four ways, mentioned by Cremona.^ 



It may be required to multiply a segment by a series of quantities 

 successively. This may be done by various constructions, of which 

 Cremona, Favaro, and others give several. The process in all cases 

 simply consists in a repetition of ordinary multiplication, the construction 

 being modified for the sake of convenience. 



The quantity by which a segment may be required to be multiplied 

 may be numerically equal to itself, in which case (which is equivalent to 



' P. 49 et seq., English translation. 



